| ∀ x0 : ((ι → ι) → (ι → ι) → ι) → ι → ι → ι . ∀ x1 : (ι → ι → ((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι → ι . ∀ x2 : ((ι → ι → ι) → ι → ι) → ι → (ι → ι → ι) → ι . ∀ x3 : (ι → ι) → ι → (((ι → ι) → ι) → ι) → ι . (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . x3 (λ x9 . Inj0 (setsum 0 (Inj1 x9))) (setsum 0 x4) (λ x9 : (ι → ι) → ι . x5) = setsum (x1 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . x0 (λ x12 x13 : ι → ι . Inj1 (setsum 0 0)) (Inj1 0) (x0 (λ x12 x13 : ι → ι . x2 (λ x14 : ι → ι → ι . λ x15 . 0) 0 (λ x14 x15 . 0)) (Inj0 0) (x7 0 (λ x12 : ι → ι . λ x13 . 0) (λ x12 . 0)))) (λ x9 x10 . 0) (setsum x5 (x7 x4 (λ x9 : ι → ι . λ x10 . x2 (λ x11 : ι → ι → ι . λ x12 . 0) 0 (λ x11 x12 . 0)) (λ x9 . x6 0)))) 0) ⟶ (∀ x4 . ∀ x5 : ((ι → ι → ι) → ι) → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → (ι → ι) → ι) → ι . x3 (λ x9 . x1 (λ x10 x11 . λ x12 : (ι → ι) → ι → ι . x12 (λ x13 . x2 (λ x14 : ι → ι → ι . λ x15 . x3 (λ x16 . 0) 0 (λ x16 : (ι → ι) → ι . 0)) (setsum 0 0) (λ x14 x15 . x12 (λ x16 . 0) 0)) (x0 (λ x13 x14 : ι → ι . x13 0) (setsum 0 0) x11)) (λ x10 . Inj0) (x1 (λ x10 x11 . λ x12 : (ι → ι) → ι → ι . x3 (λ x13 . 0) (x2 (λ x13 : ι → ι → ι . λ x14 . 0) 0 (λ x13 x14 . 0)) (λ x13 : (ι → ι) → ι . x2 (λ x14 : ι → ι → ι . λ x15 . 0) 0 (λ x14 x15 . 0))) (λ x10 x11 . x0 (λ x12 x13 : ι → ι . x2 (λ x14 : ι → ι → ι . λ x15 . 0) 0 (λ x14 x15 . 0)) (x0 (λ x12 x13 : ι → ι . 0) 0 0) (setsum 0 0)) (Inj0 x9))) x6 (λ x9 : (ι → ι) → ι . Inj1 0) = Inj0 (x7 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . x3 (λ x11 . Inj1 (Inj0 0)) 0 (λ x11 : (ι → ι) → ι . Inj1 (x10 0))))) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 x6 . ∀ x7 : (ι → ι) → ((ι → ι) → ι → ι) → ι . x2 (λ x9 : ι → ι → ι . λ x10 . setsum 0 (x7 (x0 (λ x11 x12 : ι → ι . x0 (λ x13 x14 : ι → ι . 0) 0 0) (x0 (λ x11 x12 : ι → ι . 0) 0 0)) (λ x11 : ι → ι . λ x12 . Inj0 (Inj1 0)))) (x7 (λ x9 . x5) (λ x9 : ι → ι . λ x10 . setsum (x3 (λ x11 . x3 (λ x12 . 0) 0 (λ x12 : (ι → ι) → ι . 0)) 0 (λ x11 : (ι → ι) → ι . 0)) x6)) (λ x9 x10 . setsum 0 0) = x7 (λ x9 . x6) (λ x9 : ι → ι . λ x10 . setsum (x2 (λ x11 : ι → ι → ι . λ x12 . x3 (λ x13 . setsum 0 0) (setsum 0 0) (λ x13 : (ι → ι) → ι . 0)) (Inj0 0) (λ x11 x12 . x9 (setsum 0 0))) (x3 (λ x11 . x3 (λ x12 . Inj1 0) (x1 (λ x12 x13 . λ x14 : (ι → ι) → ι → ι . 0) (λ x12 x13 . 0) 0) (λ x12 : (ι → ι) → ι . 0)) (Inj0 x6) (λ x11 : (ι → ι) → ι . x2 (λ x12 : ι → ι → ι . λ x13 . setsum 0 0) (x1 (λ x12 x13 . λ x14 : (ι → ι) → ι → ι . 0) (λ x12 x13 . 0) 0) (λ x12 x13 . 0))))) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x7 . x2 (λ x9 : ι → ι → ι . λ x10 . x7) x5 (λ x9 x10 . x0 (λ x11 x12 : ι → ι . x11 (x2 (λ x13 : ι → ι → ι . λ x14 . setsum 0 0) 0 (λ x13 x14 . setsum 0 0))) 0 (x2 (λ x11 : ι → ι → ι . λ x12 . setsum (x3 (λ x13 . 0) 0 (λ x13 : (ι → ι) → ι . 0)) (x2 (λ x13 : ι → ι → ι . λ x14 . 0) 0 (λ x13 x14 . 0))) (setsum (x2 (λ x11 : ι → ι → ι . λ x12 . 0) 0 (λ x11 x12 . 0)) (x6 (λ x11 : (ι → ι) → ι → ι . 0) (λ x11 : ι → ι . 0) (λ x11 . 0) 0)) (λ x11 x12 . x0 (λ x13 x14 : ι → ι . x13 0) (x2 (λ x13 : ι → ι → ι . λ x14 . 0) 0 (λ x13 x14 . 0)) (x0 (λ x13 x14 : ι → ι . 0) 0 0)))) = x0 (λ x9 x10 : ι → ι . x7) (x2 (λ x9 : ι → ι → ι . λ x10 . setsum (setsum (Inj1 0) (x0 (λ x11 x12 : ι → ι . 0) 0 0)) 0) 0 (λ x9 x10 . x3 (λ x11 . 0) x10 (λ x11 : (ι → ι) → ι . x10))) x5) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x1 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . 0) (λ x9 x10 . setsum (setsum (Inj0 (x0 (λ x11 x12 : ι → ι . 0) 0 0)) (setsum 0 (x2 (λ x11 : ι → ι → ι . λ x12 . 0) 0 (λ x11 x12 . 0)))) (setsum (x7 (x2 (λ x11 : ι → ι → ι . λ x12 . 0) 0 (λ x11 x12 . 0))) x9)) (x3 (λ x9 . x3 (λ x10 . 0) x5 (λ x10 : (ι → ι) → ι . x9)) (Inj1 (Inj1 (setsum 0 0))) (λ x9 : (ι → ι) → ι . x2 (λ x10 : ι → ι → ι . λ x11 . x10 (x0 (λ x12 x13 : ι → ι . 0) 0 0) (Inj0 0)) 0 (λ x10 x11 . x1 (λ x12 x13 . λ x14 : (ι → ι) → ι → ι . setsum 0 0) (λ x12 x13 . Inj0 0) (setsum 0 0)))) = Inj1 (Inj1 x6)) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι → ι) → ι . ∀ x5 x6 x7 . x1 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . 0) (λ x9 x10 . 0) 0 = x7) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι . ∀ x7 : ι → ι → (ι → ι) → ι → ι . x0 (λ x9 x10 : ι → ι . x7 (Inj0 0) (x9 (x2 (λ x11 : ι → ι → ι . λ x12 . Inj0 0) (x1 (λ x11 x12 . λ x13 : (ι → ι) → ι → ι . 0) (λ x11 x12 . 0) 0) (λ x11 x12 . x1 (λ x13 x14 . λ x15 : (ι → ι) → ι → ι . 0) (λ x13 x14 . 0) 0))) (λ x11 . x0 (λ x12 x13 : ι → ι . 0) (x2 (λ x12 : ι → ι → ι . λ x13 . 0) 0 (λ x12 x13 . 0)) (x2 (λ x12 : ι → ι → ι . λ x13 . x12 0 0) (Inj0 0) (λ x12 x13 . x1 (λ x14 x15 . λ x16 : (ι → ι) → ι → ι . 0) (λ x14 x15 . 0) 0))) (x0 (λ x11 x12 : ι → ι . Inj0 (setsum 0 0)) (x10 (x0 (λ x11 x12 : ι → ι . 0) 0 0)) (x0 (λ x11 x12 : ι → ι . x11 0) (x9 0) (x0 (λ x11 x12 : ι → ι . 0) 0 0)))) 0 0 = setsum (setsum (setsum x5 (x2 (λ x9 : ι → ι → ι . λ x10 . x3 (λ x11 . 0) 0 (λ x11 : (ι → ι) → ι . 0)) (x1 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . 0) (λ x9 x10 . 0) 0) (λ x9 x10 . x9))) 0) (x7 (setsum (x7 (setsum 0 0) (x7 0 0 (λ x9 . 0) 0) (λ x9 . x1 (λ x10 x11 . λ x12 : (ι → ι) → ι → ι . 0) (λ x10 x11 . 0) 0) 0) (x0 (λ x9 x10 : ι → ι . x6 0 0) (x3 (λ x9 . 0) 0 (λ x9 : (ι → ι) → ι . 0)) (setsum 0 0))) (x6 0 (setsum (x0 (λ x9 x10 : ι → ι . 0) 0 0) (setsum 0 0))) (λ x9 . x2 (λ x10 : ι → ι → ι . λ x11 . x0 (λ x12 x13 : ι → ι . 0) 0 (x2 (λ x12 : ι → ι → ι . λ x13 . 0) 0 (λ x12 x13 . 0))) 0 (λ x10 x11 . x7 x9 (x3 (λ x12 . 0) 0 (λ x12 : (ι → ι) → ι . 0)) (λ x12 . 0) 0)) (Inj0 (x7 (x3 (λ x9 . 0) 0 (λ x9 : (ι → ι) → ι . 0)) (x0 (λ x9 x10 : ι → ι . 0) 0 0) (λ x9 . x7 0 0 (λ x10 . 0) 0) (x1 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . 0) (λ x9 x10 . 0) 0))))) ⟶ (∀ x4 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : ι → ((ι → ι) → ι → ι) → ι . x0 (λ x9 x10 : ι → ι . 0) 0 0 = x7 (x0 (λ x9 x10 : ι → ι . x9 (x0 (λ x11 x12 : ι → ι . x12 0) (Inj0 0) (x6 0))) (Inj1 0) (x0 (λ x9 x10 : ι → ι . x0 (λ x11 x12 : ι → ι . x3 (λ x13 . 0) 0 (λ x13 : (ι → ι) → ι . 0)) 0 (x10 0)) x5 (x4 (x1 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . 0) (λ x9 x10 . 0) 0) (λ x9 : ι → ι . λ x10 . setsum 0 0) (λ x9 . 0) (x1 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . 0) (λ x9 x10 . 0) 0)))) (λ x9 : ι → ι . λ x10 . x3 (λ x11 . x11) (Inj0 (setsum (setsum 0 0) (Inj1 0))) (λ x11 : (ι → ι) → ι . 0))) ⟶ False |
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